Mathematics is not a deductive science - that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.

I read once that the true mark of a pro - at anything - is that he understands, loves, and is good at even the drudgery of his profession.

The only way to learn mathematics is to do mathematics.

The beginner should not be discouraged if he finds he does not have the prerequisites for reading the prerequisites.

Mathematics is not a deductive science - that's a cliché... What you do is trial and error, experimentation, guesswork.

A smooth lecture... may be pleasant; a good teacher challenges, asks, irritates and maintains high standards - all that is generally not pleasant.

You are allowed to lie a little, but you must never mislead.